Whilst I have a certain alignment to the "its my choice" type mentality sometimes people will not / do not understand the impacts on them from what they do, and those sorts of people either need encouragement to change or have to be forced to.
Food is very clear cut, heavily processed and cheap foods will contain more bad stuff because thats cheap and helps to mask the flavour of other poor quality ingredients.
But the issue I see is working out the boundaries, if you force up the costs of a cheap calorie laden sausage roll to the point its not worth buying then you will by default force up the costs of the good meat that came from the same supply.
Eg if a cow cost £100 and the cheap rubbish meat was sold for £10 then you would need to sell the rest for £90 (lets assume your just breakin even for now). If the cheap rubbish bits became unwanted then you would need to charge £100 for the good stuff.
Some areas are different, you do not need sugar in drinks but they make them more palateable to a lot of people. Its just like adding sugar to a cup of tea or coffee.
I rarely eat takeaway, to me its more like a treat, it always was but then I am of an age where McDs were not in the town when I was really young. Literally all the fast food restaurants appeared in the town I grew up in between the ages of 12-16 or so. The only fast food before that was KFC and Wimpey, KFC at those times was expensive so was a real treat not an alternative to "normal food".
People like eating, well a lot do. I am not sure if taxing it will change that unless it becomes so expensive you cannot afford to, but again to significantly affect the ability of a large part of the population from over eating you would need a massive increase in food prices further trying to force the middle down to the bottom as you would have to increase benefits to be able to live.
The only way I could see some sense would be to abandon current VAT rules (where basic items are VAT free and "luxury" items taxed). I remember them adding VAT to takeaways as they were not even taxed till about 1983 or something like that. With no VAt being charged then you could implement a sliding scale of tax based on calorific value per 100g. Highly processed and high calorie added foods would suffer a much higher loading which would probably trigger manufacturers to try to reduce these items and use better premium ingredients and hence need less addatives.
Certainly in the US the corn syrup industry is powerful and the product is cheap, this acts as a barrier to entry for alternatives be that natural or synthetic since they are more expensive. There was some stuff on this in a BBC documentary series last year. Think it was called the truth about food.